SCHENECTADY — Nearly a year after 15 Schenectady nonprofit groups missed the deadline to file for their annual tax exemption, the governor has begun forgiving their taxes.

On Thursday, Gov. David Paterson signed the first of six bills intended to restore the tax exemption of city nonprofits. Legislative aides said it was a precedent-setting decision that would clear the way for all 15 nonprofits to escape their tax bills and possibly even get refunds for taxes they have already paid.

The only nonprofit that was forgiven Thursday was Schenectady Home Furnishings Inc., which collects used furniture and gives it to needy families, including fire victims.

The governor is expected to sign the other bills soon. They all relate to the same issue, but each names a different nonprofit.

It’s been a long, stressful year for the nonprofit directors who were named in the bills. They joked that they have learned more about the state legislative process than they ever wanted to know.

First they begged the city for help, then took their case to Sen. Hugh Farley, R-Niskayuna, and Assembly Minority Leader James Tedisco, R-Schenectady.

The men agreed to champion their cause, but once the bills passed the Senate, they dropped into the Assembly Rules Committee, where one version of the bills still remains.

Another version — breaking the bill apart so that each nonprofit was named separately — passed the Assembly. But Don Leach of Home Furnishings Inc. nearly panicked when he checked on the original bill at the end of the session and saw it had been abandoned in Rules. He hadn’t realized a different bill had passed.

Then came the long wait to see whether the governor would sign the bills. Yesterday, Leach lost hope, thinking the governor has missed the deadline to sign or veto them.

“I kept watching the Web site for the list of signed bills, and we had heard the deadline was yesterday,” Leach said after learning that the governor had indeed signed the bill on time.

“I am very, very much relieved.”

His agency was assessed a tax bill of $5,500 — an almost insurmountable bill on an annual budget of $40,000.

“It’s about one-third of the contributions we get in an entire year,” Leach said.

Although he can now avoid the final payments for this year, he has already paid $1,400. The jury is still out on whether the city will refund the taxes.

The Schenectady City Council has not yet discussed it.

“I would like to get a refund, but I understand it’s their choice,” Leach said.

Schenectady Home Furnishings Inc. was one of the lucky ones. Only six of the 15 taxed nonprofits were included in the state legislation.

Farley and Tedisco filed the bills for every nonprofit they were aware of, but could not get a complete list from the city. They now have the full list and are expected to craft bills for all of them.